Negative Binomial Distribution

The negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of Bernoulli trials before a specified (non-random) number r of failures occurs.

The negative binomial distribution also arises as a continuous mixture of Poisson distributions where the mixing distribution of the Poisson rate is a gamma distribution. The variance differs from the Poisson distribution and is modeled as:

V(µ) = µ + a*µ2

where µ is the mean and a is the dispersion parameter.

In STATISTICA, you can specify negative binomial as the distribution for a generalized linear model with a dispersion parameter of greater than or equal to 0. An entered value of zero means the dispersion parameter is estimated via maximum likelihood. Otherwise, the entered constant value is used for the dispersion parameter.